Question

A Gallup poll found that only $28\%$of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a $95\%$confidence level. This means that

a. the poll used a method that gets an answer within 3% of the truth about the population $95\%$of the time.

b. the percent of all adults who expect an inheritance must be between $25\%$and $31\%$.

c. if Gallup takes another poll on this issue, the results of the second poll will lie between $25\%$and $31\%$.

d. there’s a 95% chance that the percent of all adults who expect an inheritance is between

25% and 31%.

e. Gallup can be 95% confident that between 25% and 31% of the sample expect an inheritance.

Short answer

Option (b) is correct.

Step-by-step solution

Given Information

It is given that $\left(\hat{p}\right)=28\%=0.28$

$\left(E\right)=3\%=0.03$

Concept Used

Formula to be used:

$CI=\hat{p}\pm E$

Calculation

Confidence Interval is calculated as:

$CI=\hat{p}\pm E==0.28\pm 0.03$

$CI=(0.25,0.31)$

Hence, option (b) is correct.